Wrote

For me units have 2 purposes:
1. Getting quickly understandable numbers
2. Checking errors (unit consistency)
...

Hi. I agree. Here, a way to get that. Also, notice that you can use almost any other unicode symbol for U(x), or 'U(x), i.e. U in blue.



DummyUnits.sm (9 KiB) downloaded 32 time(s).

Best regards.
Alvaro.

Wrote

This is where Smath is great with the possibility to use any variable as a unit. I even sometimes define units such as "bag" or "bamboo"! And doing that without using an actual "unit" but only a variable, allows to bypass Smath's unit consistency check.

That's what I have exemplified ad noseum.
However identifying what bamboo means.
Per say: approximate/discretize a PDF ... explicit result.
Pretty easy to explicit sin(30)= rad/°
Engineers manage well non SI projects.
Units war lasted years in Mathsoft Collaboratory.
Typical trig functions are approximated in rad.
What is the SI of Bessel ?

Wrote

What is the SI of Bessel ?

Bessel equations are mathematical functions.
Why should it have SI equivalence, or need units?
Unless function is used to calculate something IRL.
You are incorrectly mixing everything again.

Wrote

What is the SI of Bessel ?

The argument of the Bessel and other special functions is dimensionless, so it is the SI constant one. And the result of the Bessel and the other special functions are dimensionless too. That's the answer to you question.

But ... where do you find a physical, chemical, or any real world problem where the solution is y = Bessel(x) ? Excepting cases where x and y are angles, you will never go to get that. There are many, many examples where the solution is in the form y = A*Bessel(k*x) or lineal combinations of such solutions, where A have the units for the variable y, and k have the inverse of the units of x.

For a simple example, a mechanical oscillation could be y = A*sin(ω*t), with y and A in mm and t in sec and ω in Hz. More or less the same for the current in an electrical circuit if I = Io*sin(ω*t+φ)

That is the correct way in which millions of scientists, technicians, engineers and workers have been doing things for thousands of years: working with magnitudes and their units. This collection standards came from the ancient Egypt: https://upload.wikimedia.org/wikipedia/commons/6/65/Louvres-antiquites-egyptiennes-img_2748.jpg

If you know how, all mathematical functions can be manipulated with their corresponding units, when dealing with real world problems. So please stop confusing users with arguments that border on flat earthing.

Best regards.
Alvaro.

Wrote

What is the SI of Bessel ?

Answer: the fitted data Bessel will have unit of the data source.
Some fitted projects were done in Smath Forum.
No need to complain +

Wrote

Answer: the fitted data Bessel will have unit of the data source.

What will be your next 'ad hominem" request, SI version for Pythagorean Theorem?
You know, it is originally a mathematical function but it can have units.
There are a lot of fitted projects were done with SI unit, want some examples?

A unit Bessel function is as just Razonar said, A x Bessel(x). Which A is a unit or unitless number.

Thank you Alvaro, that's brilliant!

Thanks also for the Egyptian "measurement scale"! or is it one? It looks like a scale but it may be closer to what we call "slide rule"... Because I wonder on what they used this scale... Is it practical for construction, or for drawings? Was it possible to do scale drawings on papyrus? Or did they have some other supports to make drawings on?

I guess C.K. Raju's philosophy of maths will resonate with the "calculator" mentality of the Smath community:
http://ckraju.net/blog/?p=211

In his book "Euclid and Jesus" Raju wrote about the Egyptian origin of the "Elements of geometry" (In arabic, "U-Clides" = "Key to geometry") and her last and only known writer, Hypatia.

The same "calculator" approach that Jurgen Richter-Gebert has in his absolutely wonderful book, "Perspectives on Projective Geometry" which he introduces in this manner: "In a sense, this book is much more about the “how” than about the “what” in geometry."

I can't resist quoting a quote from this book:

Newsgroups: sci.math
Subject: Re: I'm looking for axioms and proof in math texts
Date: 6 Aug 2003 02:53:12 -0700
From: euclid@softcom.net (prometheus666)
[...]
and being passing familiar with the number line -- I'm sure if I don't say passing familiar somebody here will say, "You have to know vector tensor shmelaculus in 15 triad synergies to really understand the number line. It's not even called that, it's called the real
torticular space." or something to that effect --
[...]

:d

Wrote

Wrote

For me units have 2 purposes:
1. Getting quickly understandable numbers
2. Checking errors (unit consistency)
...

Hi. I agree. Here, a way to get that. Also, notice that you can use almost any other unicode symbol for U(x), or 'U(x), i.e. U in blue.



DummyUnits.sm (9 KiB) downloaded 32 time(s).

Best regards.
Alvaro.

Wrote

...
Thanks also for the Egyptian "measurement scale"! or is it one? It looks like a scale but it may be closer to what we call "slide rule"... Because I wonder on what they used this scale... Is it practical for construction, or for drawings? Was it possible to do scale drawings on papyrus? Or did they have some other supports to make drawings on?

My guess is that they made their quick calculations in sand, if they were worth it they took them to papyrus, but that those instruments were for the workers who used them in construction sites and workshops, such as looms, blacksmiths and ceramics.

Keeping those units can be very important. For example, although Eratosthenes in the III century BC said that the earth circumference is about 160,000 stadium, it is not clear whether he was referring to Greek or Egyptian stadium, which were slightly different.

Ancient data about the extension of forests or crops, sea levels, percentage of species in ecosystems can be very useful today, to address sustainable irrigation systems, as well as design the best canal layout. But if we don't know the pattern of the drives they used, the data loses much of its usefulness.

Best regards
Alvaro

Wrote

Engineers manage well non SI projects.

Wrong. All engineering is now using SI-derived units for things that include physical dimensions. That includes imperial, and all formulas where the units are implied rather than explicit.


Jean I'm annoyed that:

1. Off-topic posts and examples from you keep happening. Best to please have a separate on-topic thread for these.
   
2. There are SMath worksheets with units being overloaded (ie Ω:=1) being posted. These aren't helpful because they abuse SMath's units which isn't helpful for us noobie users.
   

I find Jean's unitless calculations very very elegant and fascinating (at least for the little that I can understand) and I am not annoyed by his bittersweet/ironic remarks here and there. We don't need to be dogmatic, or to be arbiters of taste... Everything that works, and is understandable, is good, very good! And the diversity of calculation styles that Smath Studio enables and that the creative community is pushing beyond its expected limits, are great features of this software and this forum, and its brilliant users!

I don't understand: imperial is "included" in "SI-derived units? Is that what you mean?

All the engineers I know - they are all brilliant and masters of their art - use all sorts of units: kg/cm2, MPa, tonne/m2... And they don't even care about the difference between 9.81 and 10, so 1kg = 10N and that's all !

And the building codes are full of implied units and even implied variables/dimensions.. Like the definition of the stress block, defined in 2D, the depth being implicit. So, applied strictly, the formula is badly wrong, lacking one dimension! Maybe confusing for newbies of self-taught (like me) but there's always a historical reason for such inconsistencies... I'm not saying inconsistencies are good, but it is not important. There's an art to correcting inconsistencies, keeping the whole thing clear and simple. That's the engineer's art. Not religious wars!

Wrote

Wrote

Engineers manage well non SI projects.

Wrong. All engineering is now using SI-derived units for things that include physical dimensions. That includes imperial, and all formulas where the units are implied rather than explicit.


Jean I'm annoyed that:

1. Off-topic posts and examples from you keep happening. Best to please have a separate on-topic thread for these.
   
2. There are SMath worksheets with units being overloaded (ie Ω:=1) being posted. These aren't helpful because they abuse SMath's units which isn't helpful for us noobie users.
   

My CAD drawings are in mm unit, but I draft on a feet-inches grid, with "snap" on. Because everyone here thinks in feet, not metre. But steel fabrication is in mm. So I use mm as the implied unit for drafting but my dimensions are in feet-inches for the client to understand the dimensions of his building, in mm for detailed fabrication, and in m for structural dimensions which I feed into my excel sheets (and since more recently, in Smath Studio). Because in structural calculations, having all these 12 and 144 factors all over the place is really a pain :d

Wrote

I don't understand: imperial is "included" in "SI-derived units? Is that what you mean?

All the engineers I know - they are all brilliant and masters of their art - use all sorts of units: kg/cm2, MPa, tonne/m2... And they don't even care about the difference between 9.81 and 10, so 1kg = 10N and that's all !

And the building codes are full of implied units and even implied variables/dimensions.. Like the definition of the stress block, defined in 2D, the depth being implicit. So, applied strictly, the formula is badly wrong, lacking one dimension! Maybe confusing for newbies of self-taught (like me) but there's always a historical reason for such inconsistencies... I'm not saying inconsistencies are good, but it is not important. There's an art to correcting inconsistencies, keeping the whole thing clear and simple. That's the engineer's art. Not religious wars!

Wrote

Wrote

Engineers manage well non SI projects.

Wrong. All engineering is now using SI-derived units for things that include physical dimensions. That includes imperial, and all formulas where the units are implied rather than explicit.


Jean I'm annoyed that:

1. Off-topic posts and examples from you keep happening. Best to please have a separate on-topic thread for these.
   
2. There are SMath worksheets with units being overloaded (ie Ω:=1) being posted. These aren't helpful because they abuse SMath's units which isn't helpful for us noobie users.
   

Thanks Laurent Fournier, for your appreciation.
I always give more than demanded, hoping to help new users.
Like you say, it does not deserve comments.
So often, visitors ask question(s) so badly exposed.
Take care, enjoy Smath ... Jean.

Wrote

I find Jean's unitless calculations very very elegant and fascinating.

Problem is, his calculations are hard to read. Harder to understand, illogical to revise since they are bound to certain units.
Everything is everywhere, they are color racket and there is no heuristical walkthrough in his samples.
There are even some converting numbers, strain you to understand where they come from
Which those convert numbers would be redundant if he bothered to use embedded units.
Those numbers doesn't look not very elegant on page, and not knowing where they come from at first glance is not fascinating.
And sometimes that numbers tend to make serious mistakes, like that kW/hr pump power calculation of his.
Not even a typo, he divided 1hr (3600s) to g.e (9.8), found 367 and used it in that abomination.
I have never seen that kW/hr usage anywhere, but interestingly his pump power results have it.
It should even be kW, not even kW*hr. What will be benefit of pump electrical consumption calculation?

Wrote

Everything that works, and is understandable, is good, very good!

Real problem is, some of his engineering calculations, especially unitless ones, have some serious mistakes.
Most of his viscosity related calculations are wrong due to his lack and denial of unit usage.
If he bothered and learned how to use units, he would see engineering is not just operations on given numbers.
Units and their relations are also very important to obtain correct answer at the end of some calculations.

Wrote

We don't need to be dogmatic, or to be arbiters of taste.

We wouldn't, unless he didn't propagate new users about his ridiculousness.
He wrongly claim SI units are not for engineering calculations.
I don't know what the hell this statement means, everyone in the world uses SI now.
He can use whatever he want, I personally won't care. He is a lost case.
But encouraging new users (also possibly young students) non-scientific, incorrect and illogical ways is unacceptable.

Wrote

I don't understand: imperial is "included" in "SI-derived units? Is that what you mean?

Imperial units are defined by metric (SI) units nowadays. That's what he meant.
For example, take an inch. An inch is now defined by its metric equivalent. 1 inch equals 25.4mm, nothing else.
No platinum-iridium bar used to define an inch, feet, etc now. Imperial units are based on metric units now.
Same can be said for weight definitions of imperial units or any other distinct units.
By the way, every SI unit has now abandoned man-made artifacts to define them.

https://www.youtube.com/watch?v=SmSJXC6_qQ8
https://www.youtube.com/watch?v=hid7EJkwDNk

Wrote

All the engineers I know - use all sorts of units: kg/cm2, MPa, tonne/m2... and they don't even care about the difference between 9.81 and 10, so 1kg = 10N and that's all !

All units you wrote are actually SI units. So we are saying the same thing. Using SI units will prone to less errors.
And conversions like that can be done when it is negligible, but it doesn't mean it is correct for every scenario.
It may be usable on earth, when you are going to use that conversion earth off-surface, it will definitely be wrong.

Wrote

Like the definition of the stress block, defined in 2D, the depth being implicit. So, applied strictly, the formula is badly wrong, lacking one dimension!

This is because of negligibleness when practical calculation usage is enough.
When simplification of certain functions to a certain degree won't effect the result that much, it can be done.
If you are not writing a scientific paper about stress block, there is no need to include every aspect or dimension to it.
A simplified function won't be totally wrong, it will be "correct enough".

Wrote

I am not annoyed by his bittersweet/ironic remarks here and there.

Well, we do. He makes serious mistakes and doesn't accept his failure in almost all cases.
Yet he mock requests, questions, samples, replies, try to hijack peoples topics, spam forum with same answers.
There are 10 page result if you search Colebrook, this is just ridiculous.
He once replied a question with four identical ensuing answer. Not a polite behavior.

Sorry for wall of text, Regards.

100% agree with overlord!

there is a user out there
who sadly reminds me of the dog
that comes out to bark at everyone who arrives.

Wrote

I don't understand: imperial is "included" in "SI-derived units? Is that what you mean?

Yes, that is exactly what I meant. Definition for imperial measurements no longer exists outside of SI units. Where imperial measurements are provided they are 'SI units converted to imperial using their SI definition'.

Wrote

All the engineers I know - they are all brilliant and masters of their art...

Like all sweeping generalizations, this is almost certainly wrong.

Wrote

- use all sorts of units: kg/cm2, MPa, tonne/m2... And they don't even care about the difference between 9.81 and 10, so 1kg = 10N and that's all !

I can say with a large amount of certainty that NASA, Roscosmos, SpaceX, RocketLab etc could not get away with that rounding. Perhaps it is just that they are not brilliant engineers?

Here is how dumb-ass maintaining support for imperial is... these two connectors look the same but are incompatible (5mm pitch versus 5.08mm pitch). The outside pins on the imperial compatible (0.2" ) part are 1.2mm further apart.

Connectors with less poles can kind-of work...


This type of thing looks like an industrial (process control even...) accident waiting to happen

Wrote

I can say with a large amount of certainty that NASA, SpaceX, RocketLab etc could not get away with that rounding. Perhaps it is just that they are not brilliant engineers?

Some are certainly brilliant Engineers.
However just not understood like NIST.
Many of NIST data fit made my Elephant cry...vs perfect model fit
If you have real project question, I will be there for you, Mark.
Take care ... Jean.

Wrote

Many of NIST data fit made my Elephant cry...vs perfect model fit

Possibly your "Elephants" are just scrambled-unitless-wrong calculations.
NIST data is not the culprit here presumably, your way of designing is defective.

Wrote

NIST data is not the culprit here presumably, your way of designing is defective.

Download Kirby NIST data set ... fit.
I will correct your defective design.

Wrote

Wrote

NIST data is not the culprit here presumably, your way of designing is defective.

Download Kirby NIST data set ... fit.
I will correct your defective design.

I don't have defective design.
In fact, your calculations are faulty.
You are not in position to correct someone.
Go correct your pump power calculations first!
Also don't use dynamic viscosity in your formulas.
You should use kinematic viscosity.

https://en.smath.com/forum/yaf_postst7480_Colebrook-Pipe-Data.aspx